As you would start on the number you are multiplying, when you multiply by 0, you stay on 0 (0 is external and so the arrows have no effect on 0, otherwise 0 is used as a link to create a perpetual cycle). These patterns can be used to memorize the multiples of any number from 0 to 10, except 5. Figure 2 is used for the multiples of 2, 4, 6, and 8. Some schools even remove the first column since 1 is the multiplicative identity.Ĭycles of the unit digit of multiples of integers ending in 1, 3, 7 and 9 (upper row), and 2, 4, 6 and 8 (lower row) on a telephone keypadįigure 1 is used for multiples of 1, 3, 7, and 9. In China, however, because multiplication of integers is commutative, many schools use a smaller table as below.

The illustration below shows a table up to 12 × 12, which is a size commonly used nowadays in English-world schools. Leslie also recommended that young pupils memorize the multiplication table up to 50 × 50. In his 1820 book The Philosophy of Arithmetic, mathematician John Leslie published a multiplication table up to 99 × 99, which allows numbers to be multiplied in pairs of digits at a time.

In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were 'a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144.' Modern times

The Greco-Roman mathematician Nichomachus (60–120 AD), a follower of Neopythagoreanism, included a multiplication table in his Introduction to Arithmetic, whereas the oldest surviving Greek multiplication table is on a wax tablet dated to the 1st century AD and currently housed in the British Museum. It is also called the Table of Pythagoras in many languages (for example French, Italian and Russian), sometimes in English. The multiplication table is sometimes attributed to the ancient Greek mathematician Pythagoras (570–495 BC).

Multiplication table 15x15